Lower bounds on the performance of Analog to Digital Converters
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Megretski_Lower bounds.pdf
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1.2 MB
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Author(s)
Osqui, Mitra
Megretski, Alexandre
Roozbehani, Mardavij
Date Issued
March 2012
Journal
50th IEEE Conference on Decision and Control and European Control Conference 2011 (CDC-ECC)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Osqui, Mitra, Alexandre Megretski, and Mardavij Roozbehani. “Lower Bounds on the Performance of Analog to Digital Converters.” 50th IEEE Conference on Decision and Control and European Control Conference 2011 (CDC-ECC). 1036–1041.
Version
Author's final manuscript
Abstract
This paper deals with the task of finding certified lower bounds for the performance of Analog to Digital Converters (ADCs). A general ADC is modeled as a causal, discrete-time dynamical system with outputs taking values in a finite set. We define the performance of an ADC as the worst-case average intensity of the filtered input matching error. The input matching error is the difference between the input and output of the ADC. This error signal is filtered using a shaping filter, the passband of which determines the frequency region of interest for minimizing the error. The problem of finding a lower bound for the performance of an ADC is formulated as a dynamic game problem in which the input signal to the ADC plays against the output of the ADC. Furthermore, the performance measure must be optimized in the presence of quantized disturbances (output of the ADC) that can exceed the control variable (input of the ADC) in magnitude. We characterize the optimal solution in terms of a Bellman-type inequality. A numerical approach is presented to compute the value function in parallel with the feedback law for generating the worst case input signal. The specific structure of the problem is used to prove certain properties of the value function that allow for iterative computation of a certified solution to the Bellman inequality. The solution provides a certified lower bound on the performance of any ADC with respect to the selected performance criteria.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/CDC.2011.6161525
